Check out the Reactive hypoglycemia thread on this forum. Yor symptoms sound similar to what others have posted. It would help if you could try to align your swings timewise with meals / meal timings.
By definition, RH is a disorder that causes a delayed and often excessive insulin response from the pancreas. As this was posted in the type 1 forum, I'd assume we can probably rule out RH.
This seems to be a clear case of artificial insulin management issues. Unfortunately, the ways of correcting those issues aren't always so clear.
It would be important to know things like:
When the lows are most likely to occur.
When the highs are most likely to occur.
How our friend
@KittyKat92 corrects for carbs (carb counting, sliding scale, etc)
What insulins she uses, when she uses them, and how much
Readings in excess of 20mmol/l are an obvious indication that there are times throughout the day when her body is not receiving enough insulin. The question becomes if it's the result of lack of basal or bolus insulin (or both).